PHYSICS OF COMPLEX SYSTEMS

The course aims to present a broad overview of models and of statistical and numerical techniques for the study and characterization of complex phenomena, of physical, biological and socioeconomic kind.

More specifically the objectives of the course are:

Critical understanding of the most advanced developments of Modern Physics, both theoretical and experimental, and their interrelations, also across different subjects.

Adequate knowledge of advanced mathematical and numerical tools, currently used in both basic and applied research.

Remarkable acquaintance with the scientific method, understanding of nature, and of the research in Physics.

Ability to identify the essential elements in a phenomenon, in terms of orders of magnitude and approximation level, and being able to perform the required approximations

Ability to use analytical and numerical tools, or science computing, including the development of specific software.

Ability to discuss about advanced physical concepts, both in Italian and in English.

Ability to present one's own research activity or a review topic both to an expert and to an non-expert audience.

Ability to acquire adequate tools for the continuous update of one's knowledge.

Ability to access to specialized literature both in the specific field of one's expertise, and in closely related fields.

Ability to exploit databases and bibliographical and scientific resources to extract information and suggestions to better frame and develop one's study and research activity.

Lectures and excercises in the classroom

None

Compulsory

Determinism and predictability. Deterministic chaos and sensitivity to initial conditions. Iterative maps and Hamiltonian systems. Lyapunov exponents. Kolmogorov-Sinai entropy. Strange attractors and fractal dimensions. KAM theorem. Chaos and complexity. Emergency, interdependence and self-organization. Examples of complex systems of various kinds: turbulent fluids, financial and economic systems, biological, geological and social systems. Models and numerical techniques for a quantitative study. Generalized Statistics. Superstatistics. Self-organized criticality. Methods of time series analysis. Cellular automata. Agent-based models. Models of opinion dynamics and synchronization. Efficiency of random strategies. Techniques and algorithms for numerical simulations. Complex networks. Random networks, small-world and scale-free. Characterization and main measures of centrality of complex networks.

R.C. Hilborn : Chaos and Nonlinear Dynamics Oxford University Press (1994)

J.C. Sprott: Chaos and Time-series Analysis,, Oxford University Press (2003)

E. Ott: Chaos in Dynamical systems, Cambridge University Press (1993)

F. R. Badii e A. Politi: Complexity, Cambridge University Press (1997)

Y. Bar-Yam: Dynamics of Complex systems, Westview press (1997)

Z. R.N. Mantegna e H.E. Stanley: An introduction to Econophysics, Cambridge University Press (2000)

H. Kantz e T. Schreiber : Nonlinear Time Series Analysis, Cambridge University Press (2000) S.N. Dorogovtsev e J.F.F. Mendes: Evolution of Networks,, Oxford University Press (2003)

L. Barabasi, Network Science, Cambridge University Press (2016)

Preparation of a short written dissertation on one of the topics of the programme for a general oral discussion on the main topics presented during the lectures

What is deterministic chaos and what are Lyapunov exponents ?

What is self-organized criticality?

What is the difference between chaos and complexity?

What is synchronization?

Explain the phenomenon of emergence in a complex systems

What is the difference between a random network and a scale-free one or a small world one